Linear Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

How do you write an equation for a total cost based on hourly charges?

Back

To write an equation for total cost based on hourly charges, use the formula: Total Cost = Fixed Fee + (Hourly Rate * Number of Hours).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you represent a situation with multiple items purchased at different prices?

Back

You can represent this situation with a linear equation that combines the quantities of each item multiplied by their respective prices, e.g., Price1 * Quantity1 + Price2 * Quantity2 = Total Cost.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term represents the initial value or starting point of the dependent variable when the independent variable is zero.

Front

How do you interpret the coefficients in a linear equation?

Back

Coefficients represent the amount of change in the dependent variable for a one-unit change in the independent variable.

Front

What is a real-world example of a linear equation?

Back

A real-world example of a linear equation is calculating the total cost of renting a car, where the total cost is a function of the hourly rate and the number of hours rented.

Front

How do you set up an equation for a situation involving a fixed fee and a variable cost?

Back

Set up the equation by adding the fixed fee to the product of the variable cost per unit and the number of units, e.g., Total Cost = Fixed Fee + (Variable Cost * Number of Units).